1. Field of the Invention
The present invention relates to a diffractive optical element comprising a plurality of layers stacked one another to form at least one boundary surface formed by adjacent layers made of different optical materials, and a relief pattern formed in said boundary surface, and more particularly to a diffractive optical element having a decreased wavelength dependency of diffraction efficiency for a wide wavelength range.
2. Related Art Statement
The diffractive optical element of the kind mentioned above is constituted as, for instance a diffractive lens having a converging power. Such a diffractive lens has the following advantages as compared with an ordinary refractive lens.    (1) The diffractive lens can be easily produce an aspherical wave, so that aberrations can be corrected effectively.    (2) The diffractive lens does not substantially have a thickness, so that an optical system including such a diffractive lens can be made compact and a freedom of design can be improved.    (3) In the diffractive lens, a quantity corresponding to a dispersion of the refractive lens has a negative value, and thus chromatic aberration can be corrected effectively by a combination of a refractive element.
The diffractive optical element having the above advantages can improve a property of an optical system as described in, for instance Binary Optics Technology; the Theory and Design of Multi-level Diffractive Optical Element, Gary J. Swanson, Technical Report 854, MIT Lincoln Laboratory, August 1989.
As stated above, the diffractive optical element has many advantages over the ordinary refractive optical element. However, a diffractive efficiency of the diffractive optical element has a relatively large wavelength dependency, so that there are several problems to be solved. When the diffractive optical element is used as a lens element, it is undesired that there are formed a plurality of diffracted light rays, i.e. a plurality of focal points. Therefore, in a conventional diffractive lens shown in FIG. 1. a surface of a transparent substrate 1 is machined to have a sawtooth relief pattern 2 such that radiant energy is constricted to a diffracted beam having a predetermined order.
When the surface of the substrate 1 is machined to have the sawtooth cross sectional configuration as illustrated in FIG. 1, a wavelength of the diffracted beam to which radiant energy is constricted is dependent upon a depth of recesses of the relief pattern 2 (brazed relief pattern). Therefore, it is impossible to constrict the energy of the light beams within a wavelength range. This phenomenon does not cause any problem for a monochromatic radiation beam such as a laser beam, but could not be ignored for an optical system such as a camera in which white light is dealt with.
When a plurality of wavelengths are used, in order to correct a chromatic aberration a diffraction efficiency has to be optimized for a predetermined single wavelength. Then a diffraction efficiency is decreased for wavelengths other than said predetermined wavelength. Particularly, when the diffractive optical element is applied to an image pick-up optical system for picking-up a visible light image, there might be produced a variation in color and flare due to light beams of undesired orders.
FIG. 2 is a graph showing a wavelength dependency of a first order diffraction efficiency of the known diffractive optical element having the substrate 1 made of BK7 and the relief pattern 2 having such a depth that a first order diffraction efficiency becomes 100% for a wavelength λ=520 nm. As can be seen from the graph of FIG. 2, within a visible wavelength range from 400 nm to 700 nm, a diffractive efficiency becomes maximum at a wavelength of 520 nm and becomes smaller as a wavelength departs from the optimum wavelength of 520 nm. Particularly, a diffractive efficiency is decreased largely when a wavelength becomes shorter than 520 nm. Such a decrease in a diffractive efficiency for wavelengths other than the predetermined wavelength might cause undesired effect upon an optical system due to an increase in light beams of undesired orders. This apparently affects the function of the optical system including the diffractive optical element.
The relief pattern 2 having the sawtooth cross sectional shape as shown in FIG. 1 may be represented by a phase shift function φ(x) illustrated in FIG. 3. This function φ(x) characterizes a wave front modulation by the relief pattern, and can be expressed by a periodic function corresponding to the sawtooth configuration of the relief pattern. An m-order diffraction efficiency ηm of the relief pattern expressed by the phase shift function φ(x) may be given as follows:
                              η          m                =                              {                                                            sin                  ⁡                                      (                                          m                      -                      a                                        )                                                  ⁢                                                                  ⁢                π                                                              (                                      m                    -                    a                                    )                                ⁢                                                                  ⁢                π                                      }                    2                                    (        1        )            wherein a is a amplitude of variation and will be expressed as a phase amplitude hereinafter.
In the equation (1), the phase amplitude a may be defined by a the following equation:
                    a        =                                            (                              n                -                1                            )                        ⁢                                                  ⁢            d                    λ                                    (        2        )            wherein n is a refractive index of the substrate 1, d is a depth of the recess, and (λ) is a wavelength of light to be used. It should be noted that a refractive index of an air is assumed to be a unit. When a depth d0 is optimized such that a diffraction efficiency of m0 order for a wavelength λ0 becomes 100%, the depth d0 may be expressed as follows:
                              d          0                =                                            m              0                        ⁢                          λ              0                                                          n              ⁡                              (                                  λ                  0                                )                                      -            1                                              (        3        )            Then, the phase amplitude a (λ) may be represented by the following equation (4).
                              a          ⁡                      (            λ            )                          =                              m            0                    ·                                                    n                ⁡                                  (                  λ                  )                                            -              1                                                      n                ⁡                                  (                                      λ                    0                                    )                                            -              1                                ·                                    λ              0                        λ                                              (        4        )            
The above equation (4) means that for a given depth d0 the phase amplitude is dependent upon the wavelength. Due to this dependency of the phase amplitude a upon the wavelength, the wavelength dependency of the diffraction efficiency occurs as shown in FIG. 2.
The inventor has investigated the mechanism of the wavelength dependency of diffraction efficiency and has proposed a novel relief type diffractive optical element in which the wavelength dependency of diffraction efficiency is reduced. This diffractive optical element is disclosed in a co-pending U.S. patent application Ser. No. 08/522,292 filed on Sep. 7, 1995. This diffractive optical element is illustrated in FIG. 4 of the instant application. In this optical element, a first optical layer 3 made of an optical material having a high refractive index and a low dispersion and a second optical layer 4 made of an optical material having a low refractive index and a high dispersion are stacked such that a relief pattern 5 is formed in a boundary surface of these layers. It should be noted that the dispersion means a dispersion of a refractive index for a variation of a wavelength. When the relief pattern 5 is shaped into a sawtooth configuration, a phase amplitude a (λ) may be given by the following equation (5) upon optimizing the recess depth in such a manner that the diffraction efficiency of m0 order for a wavelength λ0n2(λ) becomes 100%.
                              a          ⁡                      (            λ            )                          =                              m            0                    ·                                                                      n                  1                                ⁡                                  (                  λ                  )                                            -                                                n                  2                                ⁡                                  (                  λ                  )                                                                                                      n                  1                                ⁡                                  (                                      λ                    0                                    )                                            -                                                n                  2                                ⁡                                  (                                      λ                    0                                    )                                                              ·                                    λ              0                        λ                                              (        5        )            wherein n0(λ) is a refractive index of the first optical layer 3 and n2(λ) is a refractive index of the second optical layer 4.
In the above equation (5), when n1(λ)>n2(λ) is satisfied as shown in FIG. 5 for a whole wavelength range to be used, a difference in a refractive index in a numerator becomes increased in accordance with an increase in the wavelength λ, and thus a variation of the wavelength λ in a denominator is canceled out. Therefore, the wavelength dependency of phase amplitude is reduced and thus the wavelength dependency of diffraction efficiency can be also reduced.
However, in practice, many optical materials having a large refractive index have also a large dispersion. Therefore, it is very difficult to find out a suitable combination of the first and second optical layers 3 and 4. For instance, there have been various kinds of optical materials which can be used for a visible wavelength range, but in these materials, a dispersion is increased in accordance with in increase in a refractive index. Moreover, almost all optical materials for a visible wavelength range are made of optical glasses which could not be machined easily. Therefore, when these optical glasses are combined, it is difficult to form a desired relief pattern in a boundary surface therebetween. In order to mitigate such a drawback, at least one of the optical layers may be made of optical plastic material which can be machined relatively easily. However, in such a case, plastic materials are limited and thus it is difficult to select a suitable combination of optical materials of the two optical layers 3 and 4. Particularly, it is quite difficult to improve the wavelength dependency of diffraction efficiency by a combination of two plastic materials.